Characterisation of the Free-Surface, Turbulent, Water Flows with an Array of Ultrasonic Sensors

The rough free-surface of shallow water flows such as in rivers, open channels, and pipes carries important information about the conditions of the turbulent flow, and it is related to sediment transport and mixing processes. In this paper it is shown that the spatial characteristics of the surface can be reconstructed non-invasively by measuring the reflections of airborne ultrasonic waves with an array of sensors. The phase of the signal reflected by the dynamic water surface is measured at each sensor and related to the instantaneous elevation at the specular reflection point. The reflected sound field is predicted with a numerical model based on the Kirchhoff integral. Random realisations of the rough moving surface are generated in the form of a Fourier series with the realistic spectrum and characteristic scales. These are used in a Monte Carlo simulation to predict the accuracy of the method under various surface conditions. The accuracy of the method depends on the characteristic scales of roughness and on the geometry and frequency of the system. The results can inform the design of a remote sensing device based on the scattering of airborne ultrasonic waves.